How to zip a list of files in Linux

Very simple:

zip archive -@ < out.txt

That is, if your out.txt file contains one filename per line. It will add all the files from out.txt to one archive called archive.zip.

The -@ option makes zip read from STDIN.

If you want to skip creating a temporary out.txt file, you can use grep's capability to print filenames, too. -r enables recursive search (might not be necessary in your case) and -l prints only filenames:

grep -rl "abc" file-* | zip archive -@